Could the lengths 18 in., 80 in., and 82 in. be the side lengths of a right triangle?

Answer:

Range :  {1, 3, 4, 7}

Step-by-step explanation:

Given function is defined as  f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Now we need to find about  what is the range of the given function f.

we know that y-value corresponds to the range.

since each point is written in (x,y) form so we just need to collect y-values of

f = {(2, 3), (5, 7), (3, 3), (5, 4), (9, 1)},

Hence required range is {3, 7, 3, 4, 1}

But we need to remove repeated values

so correct choice is  {1, 3, 4, 7}

Answer:

Step-by-step explanation:

y=5+2(3+4x) - Multiply parenthesis by 2

0=5+6+8x - Add the numbers

0=11+8x - Move variable to left

-8x=11 - Divide both sides by -8

x=-1.375

since the cone's diameter is 6, its radius must be 3 then.

[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi rs+\pi r^2~~ \begin{cases} r=&radius\\ s=&slant~height\\ \cline{1-2} r=&3\\ s=&5 \end{cases}\implies SA=\pi (3)(5)+\pi (3)^2 \\\\\\ SA=15\pi +9\pi \implies SA=24\pi \implies SA\approx 75.398[/tex]

Answer:

24π or 75.4

Step-by-step explanation:

The equation for the surface area is SA=πr²+πrl

Since the diameter is 6, then the radius will be 3

Plug the values in:

π3²+π×3×5

9π+15π

24π =75.39822

Answer:

Option C. 1,493

Step-by-step explanation:

If the deer population in a region is expected to decline 1.1% from 2010 to 2020. Assuming this continued, we can say that the deer population decreases 1.1% each ten years.

From 2010 to 2060 there are 50 years. If the deer population decreases 1.1% each ten years, then it will decrease 5.5% in 50 years.

If the population in 2010 was 1,578. Then, the population in 2060 is going to be:

Using the rule of three:

If 1578 ----------------> Represents 100%

    X       <-----------------       5.5%

X = (5.5%x1578)/100% = 86.79 ≈ 87

Then the total population in 2060 is: 1578 - 87 = 1491

None of the answers equal to 1491. That's why I assume the correct answer must be Option C. 1,493. Given that it's the closest answer!

Answer:

The population would be 1,493.

Step-by-step explanation:

Given,

The initial population, P = 1,578, (  In 2010 )

Also, the decline rate per 10 years, r = 1.1 %,

And, the number of the periods of 10 years since, 2010 to 2060, n = 5,

Hence, the population in 2060 would be,

[tex]A=P(1-\frac{r}{100})^n[/tex]

[tex]=1578(1-\frac{1.1}{100})^5[/tex]

[tex]=1493.09849208\approx 1493[/tex]

Option third is correct.

The specific heat capacity of the alloy is 0.423 cal/g°C: Option A is correct.

The formula for calculating the quantity of heat absorbed by the alloy is expressed as:

[tex]Q=mc\triangle \theta[/tex]

m is the mass of the substance = 45g

c is the specific heat capacity

Q is the quantity of heat required = 956J

[tex]\triangle \theta[/tex] = 37 - 25 = 12°C

Substitute the given parameters to get the specific heat capacity:

[tex]c=\frac{Q}{m \triangle \theta}\\c =\frac{956}{45 \times 12}\\c =\frac{956}{540}\\c = 1.77J/g^oC[/tex]

Convert J/g°C to  cal/g°C

c = 1.77/4.184

c = 0.423 cal/g°C

Hence the specific heat capacity of the alloy is 0.423 cal/g°C

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The specific heat of the alloy is 0.423 cal/g°C, which is calculated using the formula q = mcΔT and converting joules to calories. The final answer corresponds to option A.

The question involves finding the specific heat of an alloy using the concept of heat transfer. To calculate the specific heat, we use the formula q = mcΔT, where q is the amount of heat absorbed, m is the mass of the substance, and ΔT is the change in temperature. The specific heat c can be rearranged to be c = q/(mΔT). Given that the alloy absorbs 956 J of heat (q), has a mass of 45 g (m), and experiences a temperature increase from 25°C to 37°C (ΔT = 12°C), we plug these values into the formula.

Specific heat c will be: c = 956 J / (45 g × 12°C) = 956 J / 540 g°C = 1.77 J/g°C

To convert from joules to calories, note that 1 calorie = 4.184 joules. Thus, c in cal/g°C is calculated as: 1.77 J/g°C / 4.184 J/cal = 0.423 cal/g°C, which corresponds to option A.

Answer:

[tex]\frac{35}{2}[/tex]

Step-by-step explanation:

To solve this problem we need to write the mixed fraction as a fractional number, as follows:

[tex]3 1/3 = 3 + \frac{1}{3} = \frac{9+1}{3} = \frac{10}{3}[/tex]

[tex]5 1/4 = 5 + \frac{1}{4} = \frac{20+1}{4} = \frac{21}{4}[/tex]

Then, evaluating the expression:

[tex]\frac{10}{3}[/tex]×[tex]\frac{21}{4}[/tex] = [tex]\frac{210}{12}[/tex]

→ [tex]\frac{35}{2}[/tex]

Answer:

35 over 2

Step-by-step explanation:

Answer:

If x= 4 then f(x) = 4x -5 is 11.

Step-by-step explanation:

f(x) = 4x -5

We need to find the domain value that corresponds to the output f(x) = 11

In this question, we need to solve the expression for value of x such that the answer is 11.

if  x= 3

f(3) = 4(3) -5

     = 12 -5

    = 7

Since we want the answer 11 so we cannot take x= 3

if x = 4

f(4) = 4(4)-5

    = 16 - 5

    = 11

So, if x= 4 then f(x) = 4x -5 is 11.

Answer:

A number line with an open circle on −2, a closed circle on 5, and shading in between

Step-by-step explanation:

solve it you get x>-2

and 3x <=15

x<=5

so its close on 5 and open on -2

Answer:

T > -9/28

Step-by-step explanation:

A quadratic has two real solutions when the discriminant (b² - 4ac) is positive.

b² - 4ac > 0

3² - 4(T)(-7) > 0

9 + 28T > 0

28T > -9

T > -9/28

Answer:

The table in the attached figure N 1

The graph in the attached figure n 2

Step-by-step explanation:

we have

x+2=y

we know that

To graph a linear equation the best way is plot the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0+2=y

y=2

The y-intercept is the point (0,2)

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x+2=0

x=-2  

The x-intercept is the point (-2,0)

Find additional points to create a table (is not necessary for plot the line)

For x=1

1+2=y

y=3

For x=2

2+2=y

y=4

The table in the attached figure N 1

Graph the linear equation ------> plot the intercepts a joined the points

see the attached figure N 2

Creating a table of values for the equation \( x + 2 = y \):
To create a table of values, we can choose arbitrary values for \( x \), and then calculate the corresponding \( y \) values using the equation. Let's pick a few values for \( x \) and solve for \( y \).
Here's the table:
\[
\begin{array}{cc}
\textbf{x} & \textbf{y (= x + 2)} \\
\hline
-3 & -1 \\
-2 & 0 \\
-1 & 1 \\
0 & 2 \\
1 & 3 \\
2 & 4 \\
3 & 5 \\
\end{array}
\]
For each value of \( x \), taking the equation \( x + 2 = y \) we just add 2 to \( x \) to find \( y \).
Now, let's graph these points on a coordinate plane:
1. Draw a horizontal line for the \( x \)-axis and a vertical line for the \( y \)-axis, ensuring they intersect at the origin (0,0).
2. Mark the scale on both axes. For simplicity, we can choose each grid unit to represent 1.
3. Plot the points from the table onto the graph:
  - (-3, -1)
  - (-2, 0)
  - (-1, 1)
  - (0, 2)
  - (1, 3)
  - (2, 4)
  - (3, 5)
4. Once all the points are plotted, draw a straight line through the points, extending the line as far as the graph allows on both ends since the equation represents a linear relationship without bounds.
5. Label the line with the equation \( x + 2 = y \).
The graphical representation would show a straight line with a slope of 1 (since for every unit increase in \( x \), \( y \) increases by 1) and a \( y \)-intercept at \( y = 2 \) (since when \( x = 0 \), \( y = 2 \)).

Answer:

The sum of the first twenty-seven terms is 1,188

Step-by-step explanation:

we know that

The formula of the sum in arithmetic sequence is equal to

[tex]S=\frac{n}{2}[2a1+(n-1)d][/tex]

where

n is the number of terms

a1 is the first term

d is the common difference (constant)

step 1

Find the common difference d

we have

n=7

a1=-8

S=28

substitute and solve for d

[tex]28=\frac{7}{2}[2(-8)+(7-1)d][/tex]

[tex]28=\frac{7}{2}[-16+(6)d][/tex]

[tex]8=[-16+(6)d][/tex]

[tex]8+16=(6)d[/tex]

[tex]d=24/(6)=4[/tex]

step 2

Find the sum of the first twenty-seven terms

we have

n=27

a1=-8

d=4

substitute

[tex]S=\frac{27}{2}[2(-8)+(27-1)(4)][/tex]

[tex]S=\frac{27}{2}[(-16)+(104)][/tex]

[tex]S=\frac{27}{2}88][/tex]

[tex]S=1,188[/tex]

Answer:

3

Step-by-step explanation:

The leading coefficient is the number in front of the highest power term.

We only have one term, so the leading coefficient is 3

Answer:

26 2/3

Step-by-step explanation:

if you walked that distance 4 times last week then you walked 6 2/3 x 4

and that = 26 2/3

Answer:

x > 3

Step-by-step explanation:

Given

2(4 + 2x) < 5x + 5 ← distribute left side

8 + 4x < 5x + 5 ( subtract 5 from both sides )

3 + 4x < 5x ( subtract 4x from both sides )

3 < x ⇒ x > 3

Answer: Light waves

Step-by-step explanation:

Used in the usual sense, radiant energy is just light. When you turn on your electric stove unit, it heats up and emits radio waves, infrared waves, and visible light waves. All of these waves are just light with different frequencies.

Answer:

light waves

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The sum of the measures of all interior angles in triangle is always equal to 180°. So,

∠A+∠B+∠C=180°

∠B=180°-63°-49°=68°

Now use the sine rule:

[tex]\dfrac{c}{\sin \angle C}=\dfrac{b}{\sin \angle B}\\ \\\dfrac{3}{\sin 49^{\circ}}=\dfrac{b}{\sin 68^{\circ}}\\ \\b=\dfrac{3\sin 68^{\circ}}{\sin 49^{\circ}}\approx 3.685\approx 4[/tex]

Answer:

Its subtract 12.

Step-by-step explanation:

The first question mark is positive 6.

6-12= -6

The second question mark is  -22.

Negative 10 minus 12 equals negative 22

Once you understand integers, it will be really easy. I was in 6th grade last year.

Answer:

See graph below for answer

Step-by-step explanation:

Step 1) Change to y-intercept form

6y = 2x - 12

y = 1/3x - 2

Step 2) Graph.

See graph below for answer

Let's pretend the base price is $100

If the shopper brings enough money to cover 25% of the base price then they are bringing $25

The bargain promises 25% off of the base price of $100, meaning that the bargain price will be $75

The shopper cannot purchase the item because they only brought $25 when they should have brought $75

The shopper went home disappointed because combining a 25% off coupon and paying 25% of the base price results in a net discount of 0%, not the expected 50%.

The shopper went home disappointed because they assumed that by combining a 25% off coupon with paying 25% of the base price, they would get a 50% discount on the item. However, these discounts are applied sequentially, so the actual discount is less than 50%. In this case, the final discount would be 25% off the base price minus 25% of the base price, resulting in a net discount of 0%. The shopper didn't get the expected bargain they were hoping for because the discounts do not add up linearly but are applied to the remaining amount after the previous discount.

To know more about discount, refer here:

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Answer:

A)

62/3 = 20.67 hours

B)

60 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Part A). In 20 hr 24 minutes earth rotate 310°.

Part B). In 19 hr 6 minutes earth rotate 5 radians

Part C). 2072.4 miles point on equator rotates in 2 hours.

Step-by-step explanation:

Degree that earth rotate in 24 hour = 360°

Number of radian that earth rotate in 24 hour = 2π radian

Part A).

Time taken to rotate 360° = 24 hours

Time taken to rotate 1° = [tex]\frac{24}{360}=\frac{1}{15}\,hours[/tex]

Time taken to rotate 310° = [tex]310\times\frac{1}{15}=20\frac{2}{5}=20\,hr\:24\,minutes[/tex]

Part B).

Time taken to rotate 2π radian = 24 hours

Time taken to rotate 1 radian = [tex]\frac{24}{2\pi}=\frac{12}{\pi}\,hours[/tex]

Time taken to rotate 5 radian = [tex]5\times\frac{12}{\pi}=\frac{60}{\pi}=19.1\.hr=19\,hr\:6\,minutes[/tex]

Part C).

Diameter of Earth = 7920 miles

Radius of earth, r = 3960 miles

Degree of rotation in 1 hours = [tex]\frac{360}{24}=15^{\circ}[/tex]

Degree of rotation in 2 hours , [tex\theta[/tex] = 15 × 2 = 30°

Length of the arc for angle 30° of circle with radius 3960 miles = Distance covered by point in 2 hours.

Length of the arc = [tex]\frac{\theta}{360^{\circ}}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]

Therefore, Part A). In 20 hr 24 minutes earth rotate 310°.

                  Part B). In 19 hr 6 minutes earth rotate 5 radians

                  Part C). 2072.4 miles point on equator rotates in 2 hours.

Answer:

Step-by-step explanation:

[tex]\text{The sum of cubes:}\\\\a^3+b^3=(a+b)(a^2-ab+b^2)\\\\\text{Therefore}\\\\\text{for}\ a=6\ \text{and}\ b=s:\\\\6^3+s^3=(6+s)(6^2-6s+s^2)=(6+s)(36-6s+s^2)[/tex]

Answer: (6 + s)(s^2 – 6s + 36)

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=-\sqrt2,\ x=0,\ x=\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^3-2x=0\qquad\text{distributive}\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x^2-2=0\qquad\text{add 2 to both sides}\\\\x^2=2\to x=\pm\sqrt2[/tex]

You can factor out an x:

x ( [tex]x^{2}[/tex] - 2)

Now set x equal to zero and the expression in the parentheses equal to zero

x = 0

[tex]x^{2}  - 2 = 0[/tex]

We don't need to do anything to x = 0 because x is already isolated, but you can further isolate x in the equation:

x^2 - 2 = 0

To do this add 2 to both sides

x^2 = 2

Take the square root of both sides to completely isolate x

x = ± √2

The zeros are:

0 and ±√2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

We have the equation [tex]y=-x^2+4x-8[/tex].

We can know that this graph will have a maximum value as this is a negative parabola.

In order to find the maximum value, we can use the equation [tex]x=\frac{-b}{2a}[/tex]

In our given equation:

a=-1

b=4

c=-8

Now we can plug in these values to the equation

[tex]x=\frac{-4}{-2} \\\\x=2[/tex]

Now we can plug the x value where the maximum occurs to find the max value of the equation

[tex]y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4[/tex]

This means that the maximum of this equation is -4.

The maximum of the graph is shown to be -3

This means that the maximum value of the equation is 1 less than the maximum value of the graph

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

Answer:   173.20 ft

Step-by-step explanation:

Observe the attached image. To know how long the shadow is, we must find the length of the adjacent side in the triangle shown. Where the opposite side represents the height of the building

By definition, the function [tex]tan (x)[/tex] is defined as

[tex]tan(x) = \frac{opposite}{adjacent}[/tex]

So

[tex]opposite = 100\ feet\\x=30\°[/tex]

[tex]adjacent = l[/tex]

Then

[tex]tan(30\°) = \frac{100}{l}[/tex]

[tex]l = \frac{100}{tan(30\°)}[/tex]

[tex]l = 173.20\ ft[/tex]

The answer is:

The shadow is 173.20 feet

To solve the problem, we need to calculate the projection of the building's shadow over the ground.

We already know the height of the building (100 feet), also, we know the angle of elevation (30°), so, we can use the following formula to calculate it:

[tex]Tan(\alpha)=\frac{y}{x}=\frac{height}{x}\\\\x=\frac{height}{Tan(\alpha) }[/tex]

Now, substituting the given information and calculating, we have:

[tex]x=\frac{height}{Tan(\alpha) }[/tex]

[tex]x=\frac{100feet}{Tan(30\°) }=173.20feet[/tex]

Have a nice day!

Answer:

D. (0,5)

Step-by-step explanation:

Any points on the dashed line is not a solution. In this case, any points in the shade or above the dashed line is a solution.

For this case we must locate each of the points in the graph and see if they are in the region.

The border of the region is dotted, therefore equality is not included. That is, the points (-3,1) and (3,3) do not belong to the region.

On the other hand, we observe that the point (0,0) does not enter the region either.

Finally, it is observed that the point (0,5) if it is located within the region.

Answer:

(0,5)

Answer:

22.9m

Step-by-step explanation:

Using Pythagorean theorem, we can get two equations using the angles.

From Point A:

∠A = 20°

AB = 20m

From Point B:

∠B = 29°

BD = x

What we are looking for is the opposite side of each right triangle, each person makes because we have one adjacent side. We also know that both opposite sides will be equal.

So we use this formula for both point of views:

[tex]Tan\theta=\dfrac{Opposite}{adjacent}[/tex]

Where:

Opposite = height of the building

Adjacent = distance from the building

We are looking for the opposite side so we can tweak our formula to get an equation for the height

[tex]height=(Tan\theta)(distance)[/tex]

Using our given, we can solve for the distance of point B to D:

[tex](Tan20)(20+x) = (Tan29)(x)\\\\(0.3640)(20+x) = (0.5543)(x)\\\\\dfrac{(7.28+0.3640x)}{0.5543}=x\\\\13.1337 + 0.6567x = x\\\\13.1337 = x - 0.6567x\\\\13.1337 = 0.3433x\\\\\dfrac{13.1337}{0.3433}=x\\\\38.2572 = x[/tex]

The distance of point B to D is 38.2572 m.

Now that we know the distance of BD we can solve for the height of the building using only the given from point B.

[tex]height=(Tan\theta)(distance)[/tex]

[tex]height=(Tan29)(38.2572m)[/tex]

[tex]height=(0.5543)(38.2572m)[/tex]

[tex]height=21.21m[/tex]

But this is only the height from the line of sight. To get the height of the building from the ground, we just add the height of the viewer, which is 1.7m.

21.21m + 1.7m = 22.91m

The closest answer is: 22.91 m

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

The required polynomial would be y = x² + 38x + 311.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

Given that least degree with rational coefficients and with (-19-5√2)

We know that if a polynomial has both rational and irrational roots, the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Apply the distributive property,

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

Thus, the required polynomial would be y = x² + 38x + 311.

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Answer:

Is an equilateral triangle

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles measures 60 degrees each

so

In this problem the triangle formed by the route has three equal sides (10 miles)

therefore

Is an equilateral triangle

Answer:

[tex]64^\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{64}[/tex]

has the meaning of [tex]64^\frac{1}{4}[/tex]

That means that what you have is

[tex]64^\frac{1}{4}*^\frac{1}{3}[/tex]

which means that your final answer is

[tex]64^\frac{1}{12}[/tex]

That would be the answer that I try first. In fact the question is set up in such a way that I would ignore the fact that 64^(1/3) = 4